A few questions about upgrading my current computer, please and thank you!

I've had this computer for about 5 or so years now, changed about everything but the CPU, and Motherboard, and I thought about getting a new case. I love games, and using the computers, so I'd like this to last awhile, and be used almost daily. I work a-lot, so I really enjoy my weekends playing some games. Whenever I've replaced something in this PC, I've always came here with questions, and left with more then enough info, so thanks for the help over the years!

Currently I have,

CPU - I5- 3570k
GPU - GTX MSI 970ME
RAM - Corsair 16GB DDR3L @ 1600MHz
MotherBoard - ASRock Z77 Pro3
PSU - Corsair RM750x (Got this when the PSU that came with the computer went out)
OS - Windows 10


As you can tell, the MotherBoard and CPU are quiet old, so I wanted to upgrade them, but while I was doing that, I figure'd I'd like to get a whole new case, to change things up a bit and what not, currently using a nzxt White Phantom(One of the older ones, but still a nice case). So my main questions are,

1.
I thought about getting the Corsair Carbide Series Clear 600C because I really liked the look, and the door on the side. Has anyone that owns this tower had any issues with it?

http://www.corsair.com/en-us/carbide-series-clear-600c-inverse-atx-full-tower-case

2.
With the CPU, I always wanted to get a i7-7700k, but I did some googling(Not the best research I'm sure, but I'm not very knowledgeable when it comes to Computer Hardware, even though I love it). And it seems a great CPU that came out recently was the i5-8400 which is a bit cheaper, or even the i5-8600K which would be even better. What is your guys take on these? Are the i5-8400 or i5-8600k nice for gaming? How much better is the i5-8600k over the i5-8400? And is the i7-7700k still good with these new processors out?(I know they released a i7-8700K, but $450 is a bit high for me).

If you guys were going to get one, which would you go for, and why? Or is there a different one you'd recommend?

3.
As with the MotherBoard, I know I'll need to get a new one if I get a newer processor, and I read MSI Z370 MotherBoards are compatible with the CPU. I thought about getting the MSI Z370 GAMING M5, or Z370-A PRO depending on if theres a sale or something. And my GPU is an MSI, so I feel comfortable with that brand.

Am I right that these are the right MotherBoards? And on Amazon there are 7 different kinds, are there any real big differences in them? Or more just cosmetic and lighting things? Is one a clear winner over the others?

I found them here,
https://www.amazon.com/MSI-Z370-PRO-Coffee-Motherboard/dp/B075GVJGGW/?tag=logicaincrem-20&th=1

4.
Is my RAM compatible with these new MotherBoards and CPUs? I read on Intels website about the i5-8400, under Memory types, it lists DDR4-2666. Is that like the max, and my DDR3L-1600 will work? Or will I need some new ram?

5.
My last question, is it difficult to move a MotherBoard and CPU to a new case, or install a new one into a new case? I've never installed either a MotherBoard and CPU, I figure'd I'd watch some Youtube videos on it, or look around these forums after I figure out what hardware I needed. I know a bit about each, I know to be careful with CPUs and not to bend the pins, and to add the Thermal Compound Paste. I replaced everything else myself, but the CPU and MotherBoard are a bit intimidating with all this info about compatibility and what not. And I'd hate to ruin a brand new 200-300 dollar item that a Computer needs to work.


Thanks for reading and giving any info! I hope this wasn't to long, and doesn't seem silly. Again, thanks for any and all help, and ask any questions if I missed something, or if it'll help with your answer!